Transition from Isolates to Hybrids 2021-06

# Check requisite packages are installed.
packages <- c(
  "plotly", 
  "dplyr",
  "cheddar",
  "igraph",
  "expm",
  "foreach",
  "iterators",
  "rootSolve",
  "RMTRCode2"
)
for (pkg in packages) {
  library(pkg, character.only = TRUE)
}

# Reserved Names
communitiesAll <- NULL
invasionsDirected <- NULL
islandInteractionsOneEmptyTwo <- NULL
islandInteractionsOneEmptyTwoWhich <- NULL
islandInteractionsOneTwo <- NULL
islandInteractionsOneTwoWhich <- NULL
mats <- NULL
paramFrame <- NULL
plotScalingData <- NULL
pools <- NULL

Overview

This is the third file in the LM1996-NumPoolCom set after QDatMake-2021-05 and Questions-2021-05. These files took data sets generated from Viking for purely exploitative Lotka-Volterra systems that were assembled according to the rules from Law’s and Morton’s 1996 and 1997 papers on community assembly. The first of these organised the data sets and identified their abundances before examining how the communities compared against each other from those assembled from the same pool. Three outcomes were usually observed: one community dominated, the communities persisted but with colonies from their neighbours (sustained by mass effects), or a hybrid community emerged and dominated. The second file looked at some of the properties of the various communities we were able to observe either from the initially assembly or from the comparison. Broadly, persistence was uncommon if the system was not assembled, and some systems collapsed down to states that we had not yet observed. Hybrid systems were invadable by the regional pool again (i.e. they lost the uninvadability property). Most systems did not seem to be invadable by the other systems, where invadable from the pool is growth from an infinitesimal, but it was not uncommon to be invadable either. There are multiple ways to measure indirect effects, but (indirect) mutualism is highly uncommon in the systems created. Competition appears to be not uncommon due to interactions between basal species through their consumers.

This file returns to the context of communities interacting with each other on islands (the comparison above). Here, we want to look at how the transition occurs and if we can determine why each outcome and property emerges.

Tabs

Load Data

ellipsisApply <- function(..., FUN) {
  lapply(as.list(...), FUN)
}

load("LM1996-NumPoolCom-QOut-2021-05.RData")
# Stop if not all are not null
stopifnot(all(unlist(ellipsisApply(
  FUN = function(bool) {!is.null(bool)},
  communitiesAll,
  invasionsDirected,
  islandInteractionsOneEmptyTwo,
  islandInteractionsOneEmptyTwoWhich,
  islandInteractionsOneTwo,
  islandInteractionsOneTwoWhich,
  mats,
  paramFrame,
  plotScalingData,
  pools,
))))

plotScaling <- plotly::plot_ly(
  plotScalingData,
  x = ~Basals,
  y = ~Consumers,
  z = ~CommunitySize,
  color = ~Dataset,
  colors = c("red", "blue", "black")
)

plotScaling <- plotly::add_markers(plotScaling)

plotScaling <- plotly::layout(
  plotScaling,
  scene = list(
    xaxis = list(type = "log"),
    yaxis = list(type = "log"),
    camera = list(
      eye = list(
        x = -1.25, y = -1.25, z = .05
      )
    )
  )
)

plotScaling

Dispersal based interactions

There are 13 pools that generated multiple communities which we place on either 2 or 3 islands to generate 82 communities by looking at islands before interaction, islands while interacting near steady-state, and islands after interaction has finished. Here, we will try to look at some examples as the system transitions from the first case to the second case. Which systems should we focus on? We choose systems reflecting the various outcomes we observe.

communitiesEX <- list(
  "HybridPersists" = communitiesAll[c( 4,  5),], # Hybrid Persists.
  "HybridCollapse" = communitiesAll[c( 4,  6),], # Hybrid Collapses to persist.
  "Extinction"     = communitiesAll[c(10, 11),], # Go Extinct when uncoupled.
  "Colonies"       = communitiesAll[c( 1,  2),], # They Colonise each other.
  "Domination"     = communitiesAll[c( 7,  8),]  # One community Dominates.
)

islandFUN <- function(i, dat, pool, mat, dmat, abund = NULL) {
  temp <- dat[i, ]
  RMTRCode2::IslandDynamics(
    Pool = pool,
    InteractionMatrix = mat,
    Communities = c(
      list(temp$Communities[1]),
      rep("", nrow(dmat) - 2),
      temp$Communities[2]
    ),
    Populations = if (is.null(abund)) c(
      list(temp$CommunityAbund[1]),
      rep("", nrow(dmat) - 2),
      list(temp$CommunityAbund[2])
    ) else {
      abund
    },
    DispersalPool = 0.0001,
    DispersalIsland = dmat,
    Times = seq(from = 0, to = 2000, by = 0.1),
      # c(seq(from = 0, to = 999, by = 1), # Slow high res start
      #         seq(from = 1000, to = 20000, by = 500)) # Faster low res.
    Method = deSolve::rkMethod("rk45dp7")
  )
}

communitiesEXIslands <- lapply(communitiesEX, function(tib, pools, mats, dmat) {
  combn(
    nrow(tib), 2, 
    islandFUN,
    dat = tib, 
    pool = pools[[
      tib$DatasetID[1]
    ]][[tib$CombnNum[1]]],
    mat = mats[[
      tib$DatasetID[1]
    ]][[tib$CombnNum[1]]],
    dmat = dmat,
    simplify = FALSE
  )
}, pools = pools, mats = mats, dmat = matrix(c(
  0, 1, 0, # Island 2 -> 1
  1, 0, 1, # Island 1 -> 2, Island 3 -> 2
  0, 1, 0  # Island 2 -> 3
), nrow = 3, ncol = 3, byrow = TRUE))

Error in get(name, envir = asNamespace(pkg), inherits = FALSE) : 
  object 'partition_yaml_front_matter' not found
Error in get(name, envir = asNamespace(pkg), inherits = FALSE) : 
  object 'partition_yaml_front_matter' not found
Error in get(name, envir = asNamespace(pkg), inherits = FALSE) : 
  object 'partition_yaml_front_matter' not found

communitiesEXIslandsLong <- lapply(
  communitiesEXIslands, 
  function(listtib, islandsNum) {
    speciesNum <- (ncol(listtib[[1]]) - 1) / islandsNum
    
    retval <- tidyr::pivot_longer(
      listtib[[1]] %>% as.data.frame, 
      cols = !"time", 
      names_to = "Species",
      values_to = "Abundance"
    ) %>% dplyr::mutate(
      Species = as.numeric(Species),
      Island = floor((Species - 1) / speciesNum),
      Species = ((Species - 1) %% speciesNum) + 1 # maps 1,2,3,4 %% 4 -> 1:4
    ) %>% dplyr::group_by(
      Species, Island
    ) %>% dplyr::mutate(
      Native = dplyr::first(Abundance > 0),
      Invasive = !Native
    ) %>% dplyr::ungroup() %>% dplyr::group_by(
      Species, time
    ) %>% dplyr::mutate(
      IslandsOccupied = sum(Abundance > 0)
    ) %>% dplyr::ungroup() %>% dplyr::group_by(
      Species, Island
    ) %>% dplyr::mutate(
      Endemic = Native & dplyr::first(IslandsOccupied) == 1,
      Type = dplyr::case_when(
        Endemic ~ "Endemic",
        Native ~ "Native",
        Invasive ~ "Invasive",
        TRUE ~ "Oops"
      )
    )
    
    return(retval)
  }, islandsNum = 3
)

communitiesEXIslandsImages <- lapply(
  communitiesEXIslandsLong,
  function(tib) {
    ggplot2::ggplot(
      tib,
      ggplot2::aes(
        x = time,
        y = Abundance,
        color = as.factor(Species),
        # linetype = Type,
        group = interaction(Species, Island)
      )
    ) + ggplot2::geom_line(
    ) + ggplot2::facet_grid(
      Island ~ Type
    ) + ggplot2::scale_y_log10(
    )
  }  
)

As I am running the code and refining the images, I note that the approach to steady state appears to be extremely fast and that increasing the resolution of the integrator I am using “appears to” quicken it. Furthermore, it appears to be the case that the dynamics are changing as the time step size decreases; the oscillations are faster in cases 1 and 2 and in cases 1, 2, and 5 the outcome is different (i.e. no extinctions when the timestep is decreased.) Part of this appears to be the system resolving to much lower scales than we would consider physical; a time step of 0.1 yields some (log scale) oscillations near \(10^{-8}\). Switching methods (from “lsoda” which adapts for problem stiffness) does not appear to fix this, even if the method is adaptive in terms of time steps used (“rk45dp7” or “ode45”). Part of the problem appears to be that the tolerance, set to 0.1, is being ignored, which suggests I may be using the deSolve function(s) incorrectly. This will be the next avenue of investigation, to make sure that the tolerance is interpreted correctly.

Cases

Hybrid Persists

communitiesEXIslandsImages[[1]]

Hybrid Collapse

communitiesEXIslandsImages[[2]]

Hybrid Extincts

communitiesEXIslandsImages[[3]]

Colonies

communitiesEXIslandsImages[[4]]

Domination

communitiesEXIslandsImages[[5]]